University of Wisconsin-Madison Department of Physics: The Bicycle Wheel Gyroscope

Under the banner of “The Wonders of Physics

The article does a nice job of describing a system, the demonstrator and bicycle wheel, that conserves angular momentum about a vertical axis because it is free to rotate about a vertical axis.

It ends, however with a comment that

A motorcycle turns around corners this way. When the rider leans to one side, the whole motorcycle turns around a corner.

Motorcycles do not turn this way. Motorcycles are not free to rotate about a vertical axis because of the two tire contact patches. These generate a couple that easily alters the angular momentum of the vehicle about a vertical axis. For a similar reason, the demonstrator does not begin rotating about a horizontal axis when he tilts the bicycle wheel. His feet create a couple that prevents him from rotating about a horizontal axis and so alters the angular momentum of the system about a horizontal axis.

The actual role of gyroscopic effects in motorcycle and bicycle behavior is due instead to torque-induced precession, and this can occur in a couple of ways when the bike is rolling forward:

1. Applying a torque to the handlebars about the steering axis causes a rolling moment. For example, steering left causes a roll moment to the right. Vittore Cossalter, in his Motorcycle Dynamics​ book, describes how this can be useful in motorcycle racing.

2. Leaning the bike causes the front wheel to steer in the direction of the lean. This can contribute to, but has been shown to be not necessary​ for, the self-stability of the bike. Kooijman, et al., demonstrated this in their 2011 Science article.

The rear wheel is prevented from precessing as the front wheel does by friction of the tires on the ground, and so continues to lean as though it were not spinning at all. Hence gyroscopic forces do not provide any resistance to tipping.

I have sent an email message to the address listed at the bottom of the article, randall@physics.wisc.edu, but have not heard back.

The wonders of physics indeed. I wonder who comes up with this stuff?

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